# Group action property

From Groupprops

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This article is about a general term. A list of important particular cases (instances) is available at Category:Group action properties

## Definition

### Symbol-free definition

A **group action property** is a map from the collection of all group actions to the two-element set (true, false) with the property that if one group acts similarly on a set to another group on another set, then they get mapped to the same thing.

## Examples

### Important examples of group properties

Being transitive is a group action property: a group action is transitive if, for any two elements of the set being acted on, there is an element of the group taking one element to the other.